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Cognitive and Neural Systems Department, Boston University, Boston, Massachusetts
Submitted 19 April 2008; accepted in final form 9 August 2008
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ABSTRACT |
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INTRODUCTION |
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; DiChiara et al. 1994; Gabel and Nisenbaum 1999). Striatal DA and ACh signals each have spontaneous and learned components and both DA and ACh have been implicated as modulators of cortico-striatal learning (Centonze et al. 1999; Morris et al. 2004; Pisani et al. 2001; Wang et al. 2006; Zhou et al. 2001, 2003). Although DA is released by afferents from the midbrain, the striatum's source of ACh is intrinsic. Only giant aspiny interneurons, which are tonically active neurons (TANs) (Aosaki et al. 1994a,b, 1995; Bennett et al. 2000) release ACh. Whereas integrative models have addressed control of DA signaling, no prior model explains how striatal TAN firing patterns arise from a combination of intrinsic membrane properties, specific afferent signals, and nonspecific DAergic inputs.
Striatal TANs discharge spontaneously at 2–12 Hz in the absence of any synaptic inputs (Aosaki et al. 1995; Apicella 2002). However, they also respond to novel stimuli (Apicella et al. 1998; Ravel et al. 2001; Sardo et al. 2000), conditioned appetitive cues (Aosaki et al. 1994a,b, 1995; Ravel et al. 2001, 2003), and aversive stimuli (Apicella 2002; Ravel et al. 2003) with a brief excitation, followed by a prolonged pause and a late rebound activation (and a second pause after aversive stimuli). All or most TANs in a given part of the striatum respond synchronously to such stimuli (Aosaki et al. 1995; Apicella 2002; Apicella et al. 1998; Morris et al. 2004). Thus the firing patterns of striatal TANs are behaviorally relevant, conditionable, synchronous, and multiphasic. In the following text, we present a parametric analysis of a new computational model that robustly accounts for behavior-related electrophysiological properties of TANs, including learned responses. The model explores how inputs from striatal, cortical, thalamic, and midbrain (DAergic) neurons interact with intrinsic TAN mechanisms to adjust the striatum's cholinergic signal.
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METHODS |
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A schematic diagram of the interactions modeled in the following text is shown in Fig. 1. The model focuses on main determinants of TANs' tonic baseline activities, phasic excitations, prolonged pauses, and rebounds. The model is qualitative, and uses ordinary differential equations (ODEs) in a Hodgkin–Huxley-type formulation, modified to emphasize key dynamical properties of intrinsic currents. Model membrane voltages range from zero to one (Fig. 1, inset) and parameters were constrained to reflect empirically reported relative sizes of key parameters, such as activation thresholds (Fig. 1, inset) and the time constants for fast versus slow currents. No attempt was made to optimize curve fits, e.g., to precisely capture spiking shape. Instead, we report sensitivity analyses (see Supplementary Materials)1 that reveal the (broad) parameter ranges across which the qualitative behavior of the model is preserved and consistent with experimental reports.
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) that are subject to modulation by DA. A hyperpolarization-activated cation (HCN) current, Ih, is large enough to generate depolarization toward the membrane voltage needed for spike initiation. A tetrodotoxin (TTX)-sensitive persistent Na+ channel that operates at subthreshold membrane potential brings the membrane to firing threshold and leads to spike generation. Firing activates calcium channels. The resulting calcium voltage activates small-conductance Ca2+-dependent potassium (SK) channels that generate a medium afterhyperpolarization (mAHP; Wilson and Goldberg 2006) and a pause in cell firing. This hyperpolarization reactivates the HCN current and the cycle repeats (Bennett et al. 2000). Our presentation does not focus on spike generation and so omits TTX-sensitive sodium, large-conductance Ca2+-dependent potassium (BK), and spike-dependent calcium currents. Inclusion of these fast currents does not alter conclusions based on simulations of the simpler model (see Supplementary Materials). In vivo, these intrinsic dynamics of TANs are modulated by DA. Above a threshold, DA stimulation leads to a hyperpolarization in TANs via D2 receptors (D2Rs), activation of which reduces (depolarizing) HCN current Ih (Maurice et al. 2004; Yan et al. 1997). On the other hand, Aosaki et al. (1998) showed that DA evokes depolarization in TAN membrane through its action on D1 receptors and that such depolarization is caused by closing a resting K+ (potassium) channel and by gating a nonselective cation conductance via a cyclic adenosine monophosphate–dependent pathway.
Let V be the membrane voltage of a TAN; 
D2–dir the threshold for DA D2R activation, to exert its direct effect on intrinsic currents; and [D – D2–dir]+ and [D – D1]+ the thresholded DA actions on D2 and D1 receptors, where the value of the function [x]+ is just x if x is positive, and zero otherwise. The dynamic conductances gSK and gHCN that respectively control the voltage-dependent hyperpolarizing current SK and depolarizing current HCN (Ih) are modeled by
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 | (2) |
showed that generation of a stereotyped pause response capable of outlasting brief inputs can result from modification of the intrinsic cycle that generates spontaneous firing. A hyperpolarization-activated persistent inward-rectifying KIR current causes a pause in response to even small hyperpolarizing inputs that are above a threshold. He further argued that hyperpolarization-activated nonspecific cation (HCN) channels drive the membrane to repolarize, consistent with Bennett et al. (2000). The repolarization time constant determines the duration of the pause. Conductance for the KIR currents is here modeled by
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), SK is activated by even minute amounts of Ca2+ (Stocker et al. 2004), and KIR is a persistent K+ conductance. Thus there are no inactivation terms for these currents. The voltage-dependent activation functions h(V), f(V), and w(V) are defined by
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SK, HCN, and K define voltage thresholds for activation of conductances gSK, gHCN, and gK, respectively. Note that although SK current is activated in response to depolarization, HCN and KIR currents are activated in response to membrane hyperpolarization (Bennett et al. 2000). This difference in polarities of activation functions is reflected in the model by changes in sign (
vs. 
) of voltage thresholds for conductance activations in Eq. 4. Although SK current is Ca2+ dependent, Ca2+ dynamics are dependent on spike generation (Bennett et al. 2000; Wilson 2005), which, in turn, is dependent on voltage. Thus Eq. 1 and h(V) in Eq. 4 effectively lump together two determinants of SK channel activation by including just the primary determinant: voltage. (An unlumped model with Ca2+ dynamics and spike generation is given in the Supplementary Materials.) Activation thresholds for all currents respect the relative sizes given in the empirical literature (Fig. 1, inset).
Watanabe and Kimura (1998) showed that the effect of DA on TANs is mediated primarily via D2Rs. However, although D1-mediated effects of DA on SK (as well as KIR; see following text) currents are well known (Aosaki et al. 1998; Pisani et al. 2003), D2R-mediated modulation of K+ currents (SK and KIR) in TANs is under dispute. Thus we did not include D2R-mediated modulation of K+ currents in the base model, but we show in the Supplementary Materials that inclusion of D2R-mediated suppression of K+ currents (Yan et al. 1997) would not qualitatively alter the behavior of the TAN model. Note, though, that HCN current is robustly modulated by both D1 and D2 receptors (Maurice et al. 2004; Yan et al. 1997). Based on the kinetic properties of these two receptors (Cooper et al. 1996; Seeman 1980), it is likely that the threshold for D2R activation is lower than that for D1R activation. With D2–dir < D1, there is a phase, during the increase of striatal DA level D, during which depolarizing HCN current gHCN is suppressed, disrupting recovery of tonic firing rate (Bennett et al. 2000). The formalism used to construct model equations allowed us to capture these and similar effects dynamically (Fig. 2).
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; Lapper and Bolam 1986; Thomas et al. 2000; Yamada et al. 2004). Although direct effects of glutamatergic thalamic inputs to TANs are excitatory, thalamic input to the striatum also has a reliable inhibitory effect on cholinergic interneurons (Suzuki et al. 2001; Zackheim and Abercrombie 2005). This inhibitory input might be mediated by collaterals of MSPNs serving as relays for excitatory inputs from thalamus. However, the transmission of MSPNs is highly state dependent; their main excitatory inputs come from cortex, whereas thalamic inputs mainly terminate on interneurons (Bennett and Wilson 1998; Gerfen and Wilson 1996; Suzuki et al. 2001; Thomas et al. 2000; Yamada et al. 2004); and MSPN collateral contact with TANs may be sparse (Bolam et al. 1986; Gerfen and Wilson 1996). In contrast, thalamic inputs to GABAergic interneurons (GABA-INs) could reliably generate strong inhibitory inputs to TANs. Cortical inputs, which are exclusively glutamatergic and synapse abundantly on dendritic spines of MSPNs in the striatum, also send collaterals to GABA-INs (Bolam and Bennett 1995; Gerfen and Wilson 1996) and to distal dendrites of cholinergic interneurons (Thomas et al. 2000). These and related data (Berretta et al. 1997; Kawaguchi 1993) guided the model's treatment of excitatory thalamic and cortical inputs. Let EC and ETh be phasic, stimulus-locked, glutamatergic cortical and thalamic inputs that reach GABA-INs with latencies of CL and 50 ms, respectively, and that last for the stimulus duration ST, such that
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In the following text, we summarize evidence that the type of GABA-INs that relay such inputs to TANs, and thus provide disynaptic inhibition (cf. Suzuki et al. 2001; Zackheim and Abercrombie 2005), are nitric oxide synthase (NOS)-INs. There is a lack of definitive data regarding the direct effect of dopamine on striatal NOS-INs. However, both in parkinsonian animal models (de Vente et al. 2000; Sancesario et al. 2004) and human Parkinson's disease (Bockelmann et al. 1994; Eve et al. 1998), striatal NOS activity is depressed. Furthermore, striatal NOS-INs possess D1/D5 dopamine receptors, activation of which is excitatory (e.g., Centonze et al. 2003; Rivera et al. 2002; Sammut et al. 2006). Therefore we assume that striatal NOS-INs are directly activated by elevated DA release, although there may also be indirect pathways through which dopamine activates NOS-INs. Let V and [D – DIN]+ represent the excitation of NOS interneurons by ACh via nicotinic receptors (e.g., Consolo et al. 1999; Koos and Tepper 2002) and by (thresholded) DA via D1/D5 receptors. Then, model NOS-INs obey the following equation
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IN). A piecewise-linear signal function describes their output
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Why NOS-INs? The majority of the striatal GABAergic INs, at least in the human, are recipients of thalamic input from intralaminar nuclei to various degrees, except for calretinin-positive interneurons (CR+-INs) (Sidibe and Smith 1999). Two remaining candidates are parvalbumin-positive fast-spiking interneurons (FS-INs) and nicotinamide adenine dinucleotide phosphate (NADPH)/NOS-somatostatin-positive interneurons (NOS-INs). However, thalamic inputs to FS-INs are sparse in comparison to other asymmetric inputs, most likely of cortical origin (Rudkin and Sadikot 1999), and FS-INs have a low threshold for activation by cortical afferents (Mallet et al. 2005). Moreover, FS-INs do not make synaptic contacts with cholinergic interneurons (Bolam et al. 1986). The GABAergic NOS-INs do synapse on, and CR+-INs inhibit, cholinergic interneurons (Kubota and Kawaguchi 2000; Sullivan et al. 2008; Vuillet et al. 1992). NOS-INs are also among the main targets of thalamic afferents (Sadikot et al. 1992). Furthermore, the CM-Pf nuclei mainly project to the matrix and avoid NADPH-poor areas. These facts strongly suggest CM-Pf innervation of NOS-INs, which are estimated to be as abundant as the FS-INs (Bolam and Bennett 1995). Although NOS-INs also receive afferents from cortex, Consolo et al. (1999) showed a selective facilitation of NOS-IN activity by thalamic, but not cortical, stimulation.
This brings us to the TAN equation. In addition to medium and slow intrinsic currents (gSK, gHCN, and gK) affecting the activity of TANs, there are several external factors, including glutamatergic cortical (EC) and thalamic (ETh) inputs defined in Eqs. 5 and 6. Other external inputs to TANs include 
-aminobutyric acid (GABA) released by NOS interneurons [s(VIN); Eq. 8] and DA (D; Eq. 10) inputs from the midbrain. In addition to direct postsynaptic effects of DA on cholinergic interneurons mediated by D1Rs and D2Rs, DA has modulatory effects on other external inputs to the TANs (Flores-Hernandez et al. 2000; Nicola et al. 2000; Pisani et al. 2000), via D2Rs. In Eq. 9, which follows, this modulation is made proportional to the DA level by the multiplicative (divisive) terms (1 + β[D – D2–mod]+), acting on thalamic (ETh), cortical (EC), and NOS-IN [s(VIN)] inputs. The constant β scales this modulation. Given the intrinsic (IHCN, ISK, and IK) and synaptic (IE and II) currents implicated earlier, the activity of TANs is modeled by
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Rather than explicitly modeling activity of midbrain DA cells and DA release, diffusion, and uptake in the striatum, changes in synaptic striatal DA level are approximated by the equation
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, and IG = 0 determine the baseline DA level. The term (1 – D)ID controls phasic deviations above this baseline and IG >0 controls phasic deviations below the DA baseline. ID reflects DA neuron (DAN) bursts induced by novel or appetitive stimuli, whereas IG reflects DAN pauses induced by aversive stimuli or omissions of expected rewards. The values and timings of ID and IG obey
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Thus a phasic DA release of 50-ms duration will occur in the model with a latency of 70 ms relative to the onset of an appetitive stimulus or the offset of an aversive stimulus (see following text). The size of a real DA cell burst, and phasic DA release in the striatum, depends on prior learning (Brown et al. 1999; Redgrave et al. 1999; Schultz 1998; Tobler et al. 2005) and the bases for the learned variation have been modeled elsewhere (e.g., Brown et al. 1999; Houk et al. 1995; Suri and Schultz 1999; Tan and Bullock 2008). To reflect this dependence, the size of the phasic DA release in the model is merely scaled by ED in Eq. 11. During aversive stimuli, DANs in the ventral tegmental area (VTA) are uniformly suppressed, presumably through the action of intrinsic GABAergic cells in VTA (Ungless et al. 2004). To reflect this suppression, the inhibitory term IG is normally zero and positive only during an aversive stimulus (Eq. 12). Because such behavior of DAergic cells is controversial, a case wherein an aversive stimulus induces a DA burst, instead of uniform suppression, is treated in the Supplementary Materials.
In contrast with uniform suppression of DAergic neurons during aversive stimuli, an increase in DA release in nucleus accumbens and dorsal striatum following the offset of an aversive stimulus has been observed (Horvitz 2000; Jackson and Moghaddam 2001; Wilkinson et al. 1998; Young 2004). This DA elevation is qualitatively similar to the elevation in response to an appetitive stimulus, in terms of both its learning-dependent properties (Young 2004) and its magnitude (Feenstra et al. 2001). The increase is presumed to reflect presynaptic enhancement of DA release by glutamatergic mechanisms acting via the receptors on DA terminals (Horvitz 2000). Although such mechanisms are beyond the scope of the current model, model DA release occurs at stimulus onset if it is appetitive but at stimulus offset if it is aversive (Eq. 11).
The Fig. 1 model, as specified by Eqs. 1–12, was simulated in Matlab (The MathWorks, Natick, MA) with an adaptive fourth-order Range–Kutta method and assessed for its ability to account for the range of electrophysiological properties of striatal cholinergic interneurons (TANs) that have been observed in the experiments summarized in Table 1. The single set of parameter values used in all the simulations in RESULTS is given in Table 2. In the following, the exposition focuses on determinants of the membrane fluctuations needed to understand episodic firing-rate changes relative to the TAN baseline. To further demonstrate the generalizability of these results, the Supplementary Materials show that they are preserved in a spiking version of the model. The spiking version uses ODEs throughout, rather than a mixture of ODEs and static, voltage-dependent conductance activation curves. Although a slight departure from common practice, this approach provides a more transparent and uniformly dynamic representation of the neuron's behavior. It allows mathematical study of key effects—such as dynamic neuromodulation of conductance activations—that cannot be as readily represented and studied otherwise.
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RESULTS |
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The most conspicuous TAN response is a stereotyped pause in firing that is acquired during behavioral learning (Fig. 3A) (Aosaki et al. 1994b, 1995). This pause, often flanked by initial and rebound excitations, is cue-, but not response-, specific (Ravel et al. 2003). In striatal slices, generation of a stereotyped pause response, irrespective of the duration of relatively brief current pulses, is the result of the KIR activation that causes a pause in response to even small hyperpolarizing inputs that are above a threshold (Wilson 2005) (Fig. 4, right). Increasing the amplitude of the hyperpolarizing current pulses led to changes in the "time-to-peak" (lowest point) of the pause response. That is, the larger the current pulse, the shorter the time needed for the pause response to reach its peak. Wilson (2005) further argued that the time constant of HCN current that drives the membrane to repolarization determines the duration of the pause. The left panel of Fig. 4 shows that the dynamics of the TAN model's pause response conform with the measurements of Wilson (2005). For this set of simulations, all external inputs to TANs (NOS-IN, cortical, thalamic, and DAergic inputs) were set to zero to be consistent with utilization of striatal slices devoid of active afferents. The time-to-peak of the TAN model's pause shortens progressively with increasing amplitudes of hyperpolarizing current (Fig. 4, left). Furthermore, the pause response of the TAN model is amplified by the KIR current (gK) induced by above-threshold hyperpolarizing current (gSK), although the growth of the depression is curtailed by the model's depolarizing HCN current (gHCN), consistent with Wilson (2005).
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). Available data suggest that there may be a phasic elevation in the DA release in response to novel stimuli. As the subsequent traces in Fig. 6A show, the pause response is deepened (but not prolonged) by greater DA release. Model TANs acquire greater responsiveness to an appetitive conditioned stimulus as a result of increased DA release in the striatum at the time of conditioned stimulus onset following learning (variable ED in Eq. 11; Brown et al. 1999; Schultz 1998). In the model, the higher the DA release in the striatum, the stronger the DAergic modulation through D2Rs will be and the deeper the pause in TAN firing (Fig. 6). The amplitude of the pause response increases as the DA release in the striatum increases. This is consistent with observations (Aosaki et al. 1994b; Apicella et al. 1998) that TANs acquire their responsiveness during learning.
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). The response to an aversive stimulus includes an early pause followed by a brief activation and then a later phase of depression (Fig. 3B). Although responses of TANs to aversive stimuli vary in magnitude, it is not known whether this response modulation depended on differences in the sensory characteristics of the stimuli being presented or on differences in their aversive impact (Ravel et al. 2003). The response of the model to aversive stimuli (Fig. 5B, top plot) is consistent with the response of the cells observed experimentally (Fig. 3B). Model TANs respond to aversive stimuli with an initial facilitation, followed by a pause and rebound, and then with a second pause response. In the model, the first pause is due to the same mechanisms as for a novel stimulus, with the exception that DA levels in the model striatum (Fig. 5B, bottom plot) are suppressed during aversive stimulus presentation, consistent with Ungless (2004). Because of the relatively weakened inhibitory inputs, resulting from reduced DA during the stimulus, both the amplitude and duration of the first pause response will be less than they would be with an appetitive stimulus. Indeed, Ravel et al. (2003) showed that the amplitude of the initial depression in activity was shorter and shallower for aversive than appetitive stimuli. The suppression of DAergic baseline, however, is not crucial for the model responses (see Supplementary Materials). On stimulus offset, cortical and thalamic inputs cease; thus there is neither specific inhibition nor excitation imposed on TANs, whose activity is under the control of intrinsic mechanisms and DA. The TAN rebound firing at the stimulus offset biases the TAN membrane toward the hyperpolarization range. The phasic DA elevation acts via D2Rs to induce a second hyperpolarization, which is then augmented by KIR currents. The resultant pause is terminated by intrinsic depolarizing currents acting in tandem with the return of synaptic DA levels to baseline (Michael et al. 2005; Rebec et al. 1997; Zahniser et al. 1999).
To simulate an MPTP (1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine) lesion resulting in massive DA depletion, baseline DA level in the model (hD in Eq. 10) was set to 1% of its normal value (Schwarting and Huston 1996). As shown in Fig. 5C, the model replicates the loss of pause and rebound responses of TANs in the absence of ambient DA levels, whereas the tonic spontaneous activity is preserved. The recovery after apomorphine injection in the experiments of Aosaki et al. (1994a) is equivalent to the response of TANs to a nonhabituated novel stimulus (Fig. 6A, topmost trace), since apomorphine application locally increases DA level in the striatum and is thus equivalent to restoring the baseline DA level without any DAergic bursts in the model.
Although essential, DAergic input may not be sufficient. In a paradigm wherein they trained monkeys to learn associations between auditory and visual stimuli and liquid reward, Matsumoto et al. (2001) observed that a large majority of CM-Pf neurons respond to multimodal external stimuli with precisely timed modulations of their discharge rates. Matsumoto et al. (2001) demonstrated that the activity of CM-Pf neurons is also required for TAN expression of sensory responses to appetitive stimuli acquired through learning. After appetitive conditioning had produced learned pause responses in TANs (Fig. 3D), muscimol-induced inactivation of CM-Pf neurons virtually eliminated the pause and rebound activation of TANs. However, the initial facilitatory response of TANs was spared, with an insignificant tendency to decrease. Finally, muscimol injections in thalamus did not have a significant effect on the background, or spontaneous, activity or discharge pattern of the TANs. As shown by the simulation reported in Fig. 5D, the model is able to replicate these effects of CM-Pf inactivation. Furthermore, in their paradigm, the neurons in CM-Pf complex showed habituation if the stimulus was repeatedly presented without being followed by reward. The model implies that as the CM-Pf neurons habituate, so too will the response of TANs, consistent with Apicella (2002), who observed habituation of TAN responses in case of regular intervals in stimulus and/or reward delivery. According to the model, in the absence of CM-Pf input, NOS-INs receive glutamatergic input only from cortical projections that, by themselves, are not strong enough to cause suprathreshold activation of the NOS-INs, which are selectively facilitated by thalamic input (Eq. 8; Consolo et al. 1999). This accords with Suzuki et al. (2001), who demonstrated that cortico/thalamo-striatal stimulation induced a disynaptic inhibitory effect on TANs only when the stimulation intensity was high. With no CM-Pf input, the excitatory cortical drive to model TANs is no longer counteracted by an inhibition until the DA burst occurs. Thus during a time window of about 20 ms, from arrival of cortical input to striatum until the DA burst, cortical excitation induces an initial facilitation, albeit a weaker one than if CM-Pf input is intact. When the DA level in the striatum transiently increases as a result of the burst, however, DA not only attenuates the excitatory drive indirectly, but also directly hyperpolarizes the TAN membrane—both counteract excitation. Although the initial peak of the DA release, particularly at the advanced stages of learning, is enough to induce fluctuation in the membrane voltage, it is insufficient to exceed the threshold for KIR current engagement, as long as its magnitude is not sufficiently large to activate NOS-INs; thus no pause ensues.
However, the model shows a conditioned pause response in the absence of thalamic and cortical inputs (Fig. 6B) if a DA burst is large enough to transiently activate NOS-INs. A DA burst sufficient to induce a pause in the absence of cortical and thalamic inputs in the model is equivalent to that induced by a well-conditioned stimulus. Such a pause in response to a large-magnitude DA burst in the absence of other afferents is due to the transient DAergic facilitation of NOS-INs (Rivera et al. 2002; Sammut et al. 2006) and to the strong suppression of HCN current. The latter suppression blocks resumption of tonic firing following the transient inhibition mediated by NOS-INs. Note that in this case (no cortical or thalamic inputs), the pause duration closely follows the DAergic burst and its decay. This is consistent with the conclusion reported by Wilson (2005) that the time course of HCN current (which, in this case, tracks DA release above baseline) determines the duration of the pause.
The joint implication of variations in the strengths of thalamic and DAergic inputs is depicted in Fig. 7. For this figure, the model TAN membrane voltage (Eqs. 1–12) was computed at equilibrium for a full range of combinations of thalamic and DAergic input magnitudes while the cortical input was held constant (that model behavior is robust to different magnitudes of cortical input is shown in the Supplementary Materials). This figure proves model robustness across input combinations, but also reveals a qualitative difference in the TAN model's sensitivities to variations in thalamic versus DAergic input strengths. If thalamic activation alone is insufficient to induce a pause (a color below deep red in the scale at the right of the figure), then increases in DA release can induce pauses whose depth depends linearly on (i.e., is highly sensitive to) DA release. However, if DA release alone is insufficient to induce a pause, then a small increase in thalamic input can induce a "drop off" to a pause whose depth is almost independent of further increases in the thalamic input.
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DISCUSSION |
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, 1995; Bennett et al. 2000) and learned and unlearned responses to novel (Apicella et al. 1998; Ravel et al. 2001; Sardo et al. 2000), appetitive (Aosaki et al. 1994a,b, 1995; Ravel et al. 2001, 2003), aversive (Apicella 2002; Ravel et al. 2003), and conditioned (Aosaki et al. 1994b; Morris et al. 2004) stimuli. Other features successfully modeled here were TAN responses to current injection (Wilson 2005) and effects of eliminating either of two major afferents: glutamatergic inputs from the CM-Pf nuclei of the thalamus (Matsumoto et al. 2001) and DAergic inputs from the midbrain (Aosaki et al. 1994a). It is remarkable that all these effects can be modeled with the network of interactions shown in Fig. 1, even though it omits some features that may prove to be important in a more complete model—that is, direct inputs to TANs from the principal neurons of the striatum (MSPNs) and plastic synapses onto TANs (Suzuki et al. 2001). Indeed, a major discovery of the simulations was that all of the learned behaviors of TANs examined can be attributed to learned changes in DA signaling, consistent with Watanabe and Kimura (1998). This is due to the tight coupling between DAergic inputs and TAN responses, a coupling that engenders a reliable cascade of DA–ACh signals in striatum, which has recently been implicated in the control of striatal long-term depression (LTD; Wang et al. 2006). Thus the model highlights how DAergic projections to TANs enable many of the synaptically induced response properties of TANs. This is consistent with typical coincidences of peaks of DA bursts in substantia nigra and nadirs of TAN pauses in striatum (Morris et al. 2004). A second discovery concerns the biophysical basis of TAN pauses in response to synaptic inputs. Once a pause is initiated, DAergic modulation of the repolarizing HCN current plays a more significant role in shaping the model's pause response than previously expected. This prediction is in line with the suggestion reported by Wilson (2005) that the HCN current is one of the major determinants of the pause response in vitro. However, our model goes further to illustrate how a DA-induced bifurcation (Fig. 2) in the response of the HCN current can deepen the hyperpolarization (Fig. 6) associated with a TAN pause response in vivo without prolonging the pause beyond its normal duration. This property ensures that when a large reward has been predicted, a pause will not be "prematurely" terminated by any excitatory inputs to TANs that may occur during a TAN pause.
A third discovery was the sensitivity of model TAN behavior to a full range of two key inputs (Fig. 7). The model TAN response surface implies that within a broad range, a higher thalamic "rating" of a stimulus can often compensate for a lower DAergic "rating" of a stimulus. This may be important for two aspects of adaptive behavior. Salient novel stimuli with no reward history, which lead to large CM-Pf responses (Matsumoto et al. 2001) and modest DAergic responses (Schultz 1998), will also be able to generate a TAN pause and thereby redirect behavior (Tan and Bullock 2007). Even nonnovel (habituated) stimuli, which do not ordinarily generate large CM-Pf responses, have been shown to do so if the current task requires selective attention to, and response control by, such stimuli (Raeva 2006). Thus the ability of novelty and/or task relevance to redirect behavior, even in competition with cues with intermediate expected-reward values, may be partly mediated by CM-Pf and the TAN operating characteristic revealed in Fig. 7.
The model includes two hypotheses: 1) regarding striatal NOS-INs and 2) regarding the coupling between DA and ACh signals in response to an aversive stimulus (Fig. 5B). In the model, the pause typically follows a brief initial cue-dependent activation, induced by the short-latency cortical and thalamic inputs, which are then counteracted by lagged inhibition via NOS-INs. Thus direct excitatory and lagged disynaptic inhibitory inputs shape the TAN response, consistent with the dual projection of thalamic (and some cortical) fibers to TANs and NOS-INs (Gerfen and Wilson 1996; Lapper and Bolam 1986; Matsumoto et al. 2001; Thomas et al. 2000). However, in the absence of physiological observations from the striatum, the hypothesis of NOS-INs as key mediators of thalamic inhibition was based on sparse anatomical data and logical considerations (such as exclusion of other candidate mediators). Thus it remains possible that disynaptic inhibition of TANs is instead mediated by, or is also mediated by, another pathway, e.g., by a different GABAergic cell type. With respect to the second hypothesis, it is important to recall that the offset of an aversive stimulus serves as a reinforcer. There is a reliably observable increase in DA release in nucleus accumbens and dorsal striatum following the offset of an aversive stimulus (Horvitz 2000; Jackson and Moghaddam 2001; Wilkinson et al. 1998; Young 2004). Others have reported DA cell firing dips in VTA to aversive inputs (Ungless et al. 2004), and rebounds of accumbal DA release to offset of electrical stimulation of amygdala sites that are normally excited by aversive stimuli (Jackson and Moghaddam 2001). Consistently, enhanced release of DA in the model striatum, at the offset of the aversive stimulus, is responsible for the second pause response of the model TANs. Although not yet modeled, it is consistent that such DA release could be enhanced by cholinergic rebound to stimulus offset because nicotinic acetylcholine receptors on DA terminals boost DA release. Such a boost by cholinergic rebound is self-terminating because DA is inhibitory to TANs.
Future modeling needs to consider regional and task-related variations. Although real TANs consistently respond to behaviorally significant or conditioned stimuli with a pause, the prior brief facilitation response is sometimes robust (e.g., Morris et al. 2004), but at other times is absent (Aosaki et al. 1994b, 1995). Such variations in initial excitation might be explained in several ways. Although corticostriatal inputs are reported to provide only sparse inputs to TANs (Gerfen and Wilson 1996; Lapper and Bolam 1986; Thomas et al. 2000), variations in the balance of such inputs would affect the initial facilitation, as would the relative onset times of these inputs. As shown in Supplemental Fig. S6, the size of the initial facilitation (and the corresponding postpause rebound; see Morris et al. 2004) becomes larger in the model if there is a significant difference (whether lag or lead) between the onset times of thalamic versus cortical inputs to TANs. Regional variations in TANs' responses may be related to task effects on TANs' responses. Matsumoto et al. (2001) reported a predominance of long-latency firing (LLF) neurons in the CM, which projects to the putamen, and a relative predominance of short-latency firing (SLF) neurons in the Pf, which projects to the caudate. Pause responses to click stimuli by the TAN population in the caudate occurred earlier than in the putamen. This further implicates CM-Pf inputs to caudate and putamen as likely inducers of TAN pause responses and may be related to findings that caudate and putamen TANs are sensitive to different kinds of predictor stimuli—that is, instruction and trigger stimuli, respectively (Hikosaka et al. 1989; Kimura et al. 1984; Yamada et al. 2004).
Evidence for task effects comes from observations that more complex TAN pausing patterns emerge in instrumental conditioning protocols (Lee et al. 2006; Morris et al. 2004). Indeed, most cell activation patterns and neurotransmission signals, including DA signals (e.g., Ito et al. 2000, 2002), are more complex in instrumental tasks. The current model's scope is limited because it is based primarily on anatomical and physiological constraints and, secondarily, on observations from Pavlovian conditioning paradigms, in which cues and the rewards that they predict are under strict experimental control and do not depend on the animal's instrumental behavior. Extending the model to such behavior will be a priority as the literature on TANs and DA neurons (DANs) becomes richer in observations from instrumental paradigms. One interesting recent probe was the study of Morris et al. (2004), in which the "Pavlovian" expected value, i.e., p(reward|Cue_Identity), of a cue's identity (visual form) diverged systematically from the expected value of the cue's location, i.e., p(reward|Cue_Location), in a task in which only cue location mattered for selecting the correct instrumental response. Although the animal could perform the correct instrumental response by attending exclusively to cue location while ignoring cue identity, there was evidence that DANs in SNc and, to a smaller extent, TANs in the putamen, showed responses proportional to p(reward|Cue_Identity). Although the slope of the regression line relating cue-related firing rate changes was tenfold steeper (3 vs. 0.3) for DA cell bursts than that for TAN responses (actually averages over facilitation-pause cycles), the latter slope was still notable, with an associated r2 value of 0.99. Given the low prepause firing rates of TANs and the model's predictions of largely subthreshold effects, on TANs, of DA inputs of different sizes, these results are consistent with the present model. However, they are of indeterminate relevance. The task is more complex and the model's "Pavlovian" predictions would be better tested with methods more sensitive to subthreshold variations. A further caveat: it was not established in Morris et al. (2004) that the recorded DANs projected functional DA afferents to the putamen TANs that were recorded.
Because the pauses of model TANs are induced by DA bursts induced by unhabituated/unpredictable cues, the model can explain most known conditions for eliciting TAN pauses. Neuronal responses of TANs to rewards are more frequent and stronger when the reward is delivered at irregular, unpredictable intervals outside a task than when it predictably follows stimulus-triggered movements (Apicella et al. 1998; Sardo et al. 2000). During conditioning, TAN pauses to trigger cues are blocked or partly reduced when they are preceded by an explicit instruction (Apicella 2002). TANs respond to uncued delivery of a reward outside task contexts, but their responses to reward are reduced if it is delivered contingent on instrumental response (Ravel et al. 2001). Here the response itself renders the reward predictable. Although TANs acquire a pause to instruction cues when they precede trigger cues by a fixed interval <3 s, many of these acquired pauses were reduced if the interval between the instruction and trigger was variable or >3 s. As pauses to instruction cues declined, responses to trigger cues increased (Sardo et al. 2000). Because this behavior is what one would expect of DA bursts in these protocols, it supports the role assigned by the model to DA bursts in the genesis of conditioned TAN pauses.
Such considerations invite the hypothesis that TANs help ensure that DA signals in striatum have the properties needed by a putative internal reinforcement signal. In their critique of the reward prediction error (RPE) theory of DAN behavior, Redgrave et al. (1999) argued that DAN responses have two aspects that they did not expect of the RPE system: sensitivity to novel stimuli and insensitivity to (no dip to) conditioned aversive stimuli. The latter issue was addressed earlier. Regarding the former, it is well known that novel nonaversive events are (behaviorally) reinforcing (Mazur 1986). Also, the reinforcing property of a novel nonaversive event goes away with the passage of novelty (i.e., with habituation) unless the stimulus is a reward predictor—just as do the DAN and TAN responses to such stimuli. Indeed, if the DAN and TAN responses lacked sensitivity to novelty, that lack would make them unable to mediate the full range of reinforcing effects commonly seen in mammals. More comprehensive mathematical modeling will be needed to enable computation of the net effects of ACh–DA interactions on learning and performance functions of the striatum. However, the current model already illuminates one way that the DA–ACh coupling could work to enhance striatal learning. The striatum's high levels of dopamine transporter may indicate an adaptation to minimize the time intervals during which synaptic DA remains elevated. Elevated DA gates learning at synapses onto MSPNs and such learning may be more adaptive if restricted to short intervals after event onsets. After a reward-predicting cue, there will typically be a coincidence of four signals at MSPNs: elevated Glu release from cortico-striatal afferents, elevated DA release from nigrostriatal afferents, and elevated NOS and ACh release by striatal INs. In the model, this brief coincidence will be followed by a pause of ACh release that will last as long as the DA remains elevated. If elevated ACh serves as a gating cofactor with DA, then the time window for learning will always be very brief. This accords with the hypothesis of Morris et al. (2004) that TAN responses control the times at which plasticity is permitted. Indeed, ACh gates DA-dependent striatal LTD (Wang et al. 2006) and nitric oxide modulates striatal learning (Centonze et al. 2002).
In summary, the model proposed here is able to account for the major electrophysiological responses of striatal TANs, as recorded under normal, in vivo pathological, and slice conditions. The model's success is based on a mathematical combination of diverse mechanisms that have been separately established by anatomical and physiological methods. The model explicates interactions among inputs from striatal, cortical, thalamic, and midbrain (DAergic) neurons and intrinsic TAN mechanisms, and suggests that these interactions yield an adaptively scaled cholinergic signal. Furthermore, the model reveals an asymmetry in how novelty- and probability-sensitive mechanisms control striatal ACh release and suggests that many learning-dependent behaviors of striatal TANs are explicable without plastic changes at synapses onto TANs. This is due to the model's tight coupling between DAergic and cholinergic mechanisms. The resultant cascade of DA and ACh signals may profoundly affect striatal information processing.
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1 The online version of this article contains supplemental data. 
Address for reprint requests and other correspondence: D. Bullock. Cognitive and Neural Systems Department, Boston University, 677 Beacon Street, Boston, MA 02215 (E-mail: danb{at}cns.bu.edu)
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ABSTRACT
INTRODUCTION
